MinT - Best Known (67, 204, s)-Nets in Base 4

Best Known (67, 204, s)-Nets in Base 4

(67, 204, 66)-Net over F₄ — Constructive and digital

Digital (67, 204, 66)-net over F₄, using

t-expansion [i] based on digital (49, 204, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(67, 204, 99)-Net over F₄ — Digital

Digital (67, 204, 99)-net over F₄, using

t-expansion [i] based on digital (61, 204, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(67, 204, 492)-Net in Base 4 — Upper bound on s

There is no (67, 204, 493)-net in base 4, because

1 times m-reduction [i] would yield (67, 203, 493)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 172 614685 663587 733092 540818 600581 768374 679842 536950 479755 586239 818375 347890 942390 588689 216554 336709 803016 339968 381512 606995 > 4²⁰³ [i]