MinT - Best Known (68−35, 68, s)-Nets in Base 25

Best Known (68−35, 68, s)-Nets in Base 25

(68−35, 68, 204)-Net over F₂₅ — Constructive and digital

Digital (33, 68, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 68, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(68−35, 68, 364)-Net over F₂₅ — Digital

Digital (33, 68, 364)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−35, 68, 96654)-Net in Base 25 — Upper bound on s

There is no (33, 68, 96655)-net in base 25, because

1 times m-reduction [i] would yield (33, 67, 96655)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4591 993503 100725 457630 711126 568859 269693 673714 306233 237601 993381 340624 241729 885833 369025 522665 > 25⁶⁷ [i]