MinT - Best Known (78−44, 78, s)-Nets in Base 64

Best Known (78−44, 78, s)-Nets in Base 64

(78−44, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 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]

(78−44, 78, 519)-Net over F₆₄ — Digital

Digital (34, 78, 519)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−44, 78, 364106)-Net in Base 64 — Upper bound on s

There is no (34, 78, 364107)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 762 164657 803530 167186 696445 699063 822092 773712 370296 190789 550359 616627 648208 692896 385674 054510 633652 263612 396278 980839 895265 530092 519311 959480 > 64⁷⁸ [i]