MinT - Best Known (260−133, 260, s)-Nets in Base 4

Best Known (260−133, 260, s)-Nets in Base 4

(260−133, 260, 130)-Net over F₄ — Constructive and digital

Digital (127, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−133, 260, 176)-Net over F₄ — Digital

Digital (127, 260, 176)-net over F₄, using

t-expansion [i] based on digital (125, 260, 176)-net over F₄, using
- net from sequence [i] based on digital (125, 175)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
    - Drinfeld modules of rank 1 [i]

(260−133, 260, 1898)-Net in Base 4 — Upper bound on s

There is no (127, 260, 1899)-net in base 4, because

1 times m-reduction [i] would yield (127, 259, 1899)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 869788 806108 278461 541052 124838 181931 652412 055179 902321 545047 687346 782668 949513 409458 805060 619951 283947 382320 425551 986659 908572 450475 067364 496416 264782 050943 > 4²⁵⁹ [i]