MinT - Best Known (78−46, 78, s)-Nets in Base 64

Best Known (78−46, 78, s)-Nets in Base 64

(78−46, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (32, 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]

(78−46, 78, 199708)-Net in Base 64 — Upper bound on s

There is no (32, 78, 199709)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 762 170756 218664 976612 928777 944149 386464 164174 655514 531692 906446 800209 545337 797991 943370 462640 985576 820666 248677 027612 182110 916683 019678 351128 > 64⁷⁸ [i]