MinT - Best Known (68, 68+80, s)-Nets in Base 5

Best Known (68, 68+80, s)-Nets in Base 5

(68, 68+80, 82)-Net over F₅ — Constructive and digital

Digital (68, 148, 82)-net over F₅, using

t-expansion [i] based on digital (48, 148, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(68, 68+80, 132)-Net over F₅ — Digital

Digital (68, 148, 132)-net over F₅, using

t-expansion [i] based on digital (67, 148, 132)-net over F₅, using
- net from sequence [i] based on digital (67, 131)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(68, 68+80, 1490)-Net in Base 5 — Upper bound on s

There is no (68, 148, 1491)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 047969 703362 976316 340894 122301 104075 030175 244524 303139 077926 608332 216662 419663 788895 591673 883593 142369 > 5¹⁴⁸ [i]