MinT - Best Known (58, 87, s)-Nets in Base 8

Best Known (58, 87, s)-Nets in Base 8

Digital (58, 87, 368)-net over F₈, using

(58, 87, 520)-net in base 8, using

1 times m-reduction [i] based on (58, 88, 520)-net in base 8, using
- base change [i] based on digital (36, 66, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 33, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

Digital (58, 87, 1047)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁸⁷, 1047, F₈, 29) (dual of [1047, 960, 30]-code), using
- 959 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (5, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 36 times 0, 1, 39 times 0, 1, 42 times 0, 1, 45 times 0, 1, 49 times 0, 1, 53 times 0, 1, 57 times 0, 1, 62 times 0, 1, 67 times 0, 1, 72 times 0) [i] based on linear OA(8²⁹, 30, F₈, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,8)), using
  - dual of repetition code with length 30 [i]

There is no (58, 87, 304720)-net in base 8, because

1 times m-reduction [i] would yield (58, 86, 304720)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463177 272673 924192 420815 771613 714803 146110 396860 763252 311975 839888 896724 537287 > 8⁸⁶ [i]