MinT - Best Known (78−43, 78, s)-Nets in Base 64

Best Known (78−43, 78, s)-Nets in Base 64

(78−43, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (35, 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]

(78−43, 78, 614)-Net over F₆₄ — Digital

Digital (35, 78, 614)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−43, 78, 577835)-Net in Base 64 — Upper bound on s

There is no (35, 78, 577836)-net in base 64, because

1 times m-reduction [i] would yield (35, 77, 577836)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11 908778 707749 741203 761431 051456 271313 668856 933578 684528 516869 273846 433237 070392 126812 908169 911569 917843 640580 832206 010826 852575 214070 780764 > 64⁷⁷ [i]