MinT - Best Known (37, 37+43, s)-Nets in Base 64

Best Known (37, 37+43, s)-Nets in Base 64

(37, 37+43, 513)-Net over F₆₄ — Constructive and digital

Digital (37, 80, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 80, 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]

(37, 37+43, 744)-Net over F₆₄ — Digital

Digital (37, 80, 744)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+43, 858665)-Net in Base 64 — Upper bound on s

There is no (37, 80, 858666)-net in base 64, because

1 times m-reduction [i] would yield (37, 79, 858666)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 48778 336152 084712 975179 058528 521872 317918 327464 636915 806005 714506 903752 801440 271136 752570 238411 781266 021395 996916 455352 987244 353807 496121 478076 > 64⁷⁹ [i]