MinT - Best Known (79−30, 79, s)-Nets in Base 7

Best Known (79−30, 79, s)-Nets in Base 7

Digital (49, 79, 118)-net over F₇, using

1 times m-reduction [i] based on digital (49, 80, 118)-net over F₇, using
- trace code for nets [i] based on digital (9, 40, 59)-net over F₄₉, using
  - net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
    - Niederreiter sequence [i]

Digital (49, 79, 405)-net over F₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁷⁹, 405, F₇, 30) (dual of [405, 326, 31]-code), using
- 325 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 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, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 21 times 0, 1, 24 times 0) [i] based on linear OA(7³⁰, 31, F₇, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,7)), using
  - dual of repetition code with length 31 [i]

There is no (49, 79, 30223)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 792684 241314 509218 579432 401137 921156 620167 522358 733984 618571 752231 > 7⁷⁹ [i]