MinT - Best Known (34, 77, s)-Nets in Base 64

Best Known (34, 77, s)-Nets in Base 64

(34, 77, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 77, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 77, 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]

(34, 77, 553)-Net over F₆₄ — Digital

Digital (34, 77, 553)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 77, 474016)-Net in Base 64 — Upper bound on s

There is no (34, 77, 474017)-net in base 64, because

1 times m-reduction [i] would yield (34, 76, 474017)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 186071 005207 041396 023300 481485 729519 374889 776592 953356 978079 694674 648838 894146 406758 360234 507891 552595 537139 815767 237855 426842 766606 230688 > 64⁷⁶ [i]