MinT - Best Known (37, 37+54, s)-Nets in Base 64

Best Known (37, 37+54, s)-Nets in Base 64

(37, 37+54, 513)-Net over F₆₄ — Constructive and digital

Digital (37, 91, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 91, 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+54, 540)-Net over F₆₄ — Digital

Digital (37, 91, 540)-net over F₆₄, using

net from sequence [i] based on digital (37, 539)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 37 and N(F) ≥ 540, using
  - a curve from the manYPoints database [i]

(37, 37+54, 212096)-Net in Base 64 — Upper bound on s

There is no (37, 91, 212097)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 230 349150 183861 415265 477700 821317 754537 917599 058307 454308 613330 199870 277929 526769 262155 999688 407711 208661 667921 454537 318733 908083 260132 110262 441120 817407 116229 914240 > 64⁹¹ [i]