MinT - Best Known (79−33, 79, s)-Nets in Base 25

Best Known (79−33, 79, s)-Nets in Base 25

(79−33, 79, 288)-Net over F₂₅ — Constructive and digital

Digital (46, 79, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 79, 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]

(79−33, 79, 1522)-Net over F₂₅ — Digital

Digital (46, 79, 1522)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−33, 79, 1850474)-Net in Base 25 — Upper bound on s

There is no (46, 79, 1850475)-net in base 25, because

1 times m-reduction [i] would yield (46, 78, 1850475)-net in base 25, but
- 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]