MinT - Best Known (44, 99, s)-Nets in Base 5

Best Known (44, 99, s)-Nets in Base 5

(44, 99, 78)-Net over F₅ — Constructive and digital

Digital (44, 99, 78)-net over F₅, using

t-expansion [i] based on digital (38, 99, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(44, 99, 84)-Net over F₅ — Digital

Digital (44, 99, 84)-net over F₅, using

t-expansion [i] based on digital (43, 99, 84)-net over F₅, using
- net from sequence [i] based on digital (43, 83)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(44, 99, 920)-Net in Base 5 — Upper bound on s

There is no (44, 99, 921)-net in base 5, because

1 times m-reduction [i] would yield (44, 98, 921)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 316 668173 973291 029438 799882 373559 168620 691993 594356 528932 632299 087485 > 5⁹⁸ [i]