MinT - Best Known (93−55, 93, s)-Nets in Base 25

Best Known (93−55, 93, s)-Nets in Base 25

(93−55, 93, 208)-Net over F₂₅ — Constructive and digital

Digital (38, 93, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 93, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(93−55, 93, 211)-Net over F₂₅ — Digital

Digital (38, 93, 211)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−55, 93, 26382)-Net in Base 25 — Upper bound on s

There is no (38, 93, 26383)-net in base 25, because

1 times m-reduction [i] would yield (38, 92, 26383)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 408 083420 405158 670509 868225 427622 579166 979624 799959 887788 034968 565321 398651 874722 062502 566038 206988 225145 134013 898324 173170 941945 > 25⁹² [i]