MinT - Best Known (29, 66, s)-Nets in Base 64

Best Known (29, 66, s)-Nets in Base 64

(29, 66, 513)-Net over F₆₄ — Constructive and digital

Digital (29, 66, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 66, 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]

(29, 66, 399113)-Net in Base 64 — Upper bound on s

There is no (29, 66, 399114)-net in base 64, because

1 times m-reduction [i] would yield (29, 65, 399114)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2521 774609 085566 533227 890246 813810 030303 749653 641165 305030 123086 932426 386189 870217 463529 506368 392064 814893 619497 956160 > 64⁶⁵ [i]