MinT - Best Known (43, 91, s)-Nets in Base 64

Best Known (43, 91, s)-Nets in Base 64

(43, 91, 513)-Net over F₆₄ — Constructive and digital

Digital (43, 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]

(43, 91, 939)-Net over F₆₄ — Digital

Digital (43, 91, 939)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 91, 1097614)-Net in Base 64 — Upper bound on s

There is no (43, 91, 1097615)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 230 346247 610799 114575 527831 758503 856145 952889 159058 806972 189316 455094 457746 568660 506569 257214 115910 396820 689568 036479 364194 327911 143501 525441 313695 367514 455393 395016 > 64⁹¹ [i]