MinT - Best Known (78−45, 78, s)-Nets in Base 64

Best Known (78−45, 78, s)-Nets in Base 64

(78−45, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (33, 78, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 78, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(78−45, 78, 301388)-Net in Base 64 — Upper bound on s

There is no (33, 78, 301389)-net in base 64, because

1 times m-reduction [i] would yield (33, 77, 301389)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11 908914 255979 594370 665662 694522 226673 888013 524848 311606 183092 446404 708960 364447 787566 160055 510820 989595 802209 825766 667570 956217 888468 400080 > 64⁷⁷ [i]