MinT - Best Known (115−79, 115, s)-Nets in Base 5

Best Known (115−79, 115, s)-Nets in Base 5

(115−79, 115, 72)-Net over F₅ — Constructive and digital

Digital (36, 115, 72)-net over F₅, using

t-expansion [i] based on digital (31, 115, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(115−79, 115, 76)-Net over F₅ — Digital

Digital (36, 115, 76)-net over F₅, using

t-expansion [i] based on digital (34, 115, 76)-net over F₅, using
- net from sequence [i] based on digital (34, 75)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(115−79, 115, 397)-Net in Base 5 — Upper bound on s

There is no (36, 115, 398)-net in base 5, because

1 times m-reduction [i] would yield (36, 114, 398)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 52 591262 545056 708128 970637 210676 155745 104439 299979 292045 823121 693501 835538 580825 > 5¹¹⁴ [i]