MinT - Best Known (200−133, 200, s)-Nets in Base 4

Best Known (200−133, 200, s)-Nets in Base 4

(200−133, 200, 66)-Net over F₄ — Constructive and digital

Digital (67, 200, 66)-net over F₄, using

t-expansion [i] based on digital (49, 200, 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]

(200−133, 200, 99)-Net over F₄ — Digital

Digital (67, 200, 99)-net over F₄, using

t-expansion [i] based on digital (61, 200, 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]

(200−133, 200, 501)-Net in Base 4 — Upper bound on s

There is no (67, 200, 502)-net in base 4, because

1 times m-reduction [i] would yield (67, 199, 502)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 715231 709824 707746 070022 546556 949512 478459 012369 563648 388066 714080 529525 708976 730707 954720 266643 678074 684619 192972 613818 > 4¹⁹⁹ [i]