MinT - Best Known (76−33, 76, s)-Nets in Base 25

Best Known (76−33, 76, s)-Nets in Base 25

(76−33, 76, 288)-Net over F₂₅ — Constructive and digital

Digital (43, 76, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 76, 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]

(76−33, 76, 1130)-Net over F₂₅ — Digital

Digital (43, 76, 1130)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−33, 76, 1011970)-Net in Base 25 — Upper bound on s

There is no (43, 76, 1011971)-net in base 25, because

1 times m-reduction [i] would yield (43, 75, 1011971)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 700 656933 210153 460565 199140 979284 100083 486674 049663 903575 691539 404619 579627 117780 994943 525174 826389 231745 > 25⁷⁵ [i]