MinT - Best Known (78−42, 78, s)-Nets in Base 64

Best Known (78−42, 78, s)-Nets in Base 64

(78−42, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (36, 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]

(78−42, 78, 720)-Net over F₆₄ — Digital

Digital (36, 78, 720)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−42, 78, 704391)-Net in Base 64 — Upper bound on s

There is no (36, 78, 704392)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 762 156451 826025 034032 158861 689485 278241 047192 479534 491299 578714 448773 286168 960981 988327 525622 205354 242127 413249 295055 933650 106580 366555 639288 > 64⁷⁸ [i]