MinT - Best Known (46, 46+32, s)-Nets in Base 25

Best Known (46, 46+32, s)-Nets in Base 25

Digital (46, 78, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 78, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

Digital (46, 78, 1719)-net over F₂₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(25⁷⁸, 1719, F₂₅, 32) (dual of [1719, 1641, 33]-code), using
- 1640 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 24 times 0, 1, 27 times 0, 1, 30 times 0, 1, 33 times 0, 1, 38 times 0, 1, 41 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 64 times 0, 1, 72 times 0, 1, 79 times 0, 1, 88 times 0, 1, 98 times 0, 1, 109 times 0, 1, 121 times 0, 1, 134 times 0, 1, 150 times 0, 1, 166 times 0) [i] based on linear OA(25³², 33, F₂₅, 32) (dual of [33, 1, 33]-code or 33-arc in PG(31,25)), using
  - dual of repetition code with length 33 [i]

There is no (46, 78, 1850475)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10 947690 076359 133685 823802 118542 034112 850909 648786 592862 539023 049155 451158 260751 510620 972636 112797 836387 556481 > 25⁷⁸ [i]