MinT - Best Known (49, 49+31, s)-Nets in Base 5

Best Known (49, 49+31, s)-Nets in Base 5

(49, 49+31, 208)-Net over F₅ — Constructive and digital

Digital (49, 80, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 40, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(49, 49+31, 218)-Net over F₅ — Digital

Digital (49, 80, 218)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+31, 7697)-Net in Base 5 — Upper bound on s

There is no (49, 80, 7698)-net in base 5, because

1 times m-reduction [i] would yield (49, 79, 7698)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 16 563612 551113 407474 281893 558975 740365 907602 128951 932521 > 5⁷⁹ [i]