MinT - Best Known (38, 81, s)-Nets in Base 64

Best Known (38, 81, s)-Nets in Base 64

(38, 81, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 81, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 81, 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]

(38, 81, 819)-Net over F₆₄ — Digital

Digital (38, 81, 819)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 81, 1046726)-Net in Base 64 — Upper bound on s

There is no (38, 81, 1046727)-net in base 64, because

1 times m-reduction [i] would yield (38, 80, 1046727)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 121760 808297 671818 338350 356950 188229 577123 606517 405267 771111 274313 688320 184131 208316 827888 769139 175420 967146 120794 310048 334941 732904 031701 875752 > 64⁸⁰ [i]