MinT - Best Known (85, 85+63, s)-Nets in Base 5

Best Known (85, 85+63, s)-Nets in Base 5

(85, 85+63, 252)-Net over F₅ — Constructive and digital

Digital (85, 148, 252)-net over F₅, using

2 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(85, 85+63, 6381)-Net in Base 5 — Upper bound on s

There is no (85, 148, 6382)-net in base 5, because

1 times m-reduction [i] would yield (85, 147, 6382)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 627880 962642 407178 917664 646225 638592 093993 560496 732647 980162 676045 294751 546638 947508 115458 432294 377945 > 5¹⁴⁷ [i]