MinT - Best Known (260−139, 260, s)-Nets in Base 4

Best Known (260−139, 260, s)-Nets in Base 4

(260−139, 260, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(260−139, 260, 168)-Net over F₄ — Digital

Digital (121, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(260−139, 260, 1552)-Net in Base 4 — Upper bound on s

There is no (121, 260, 1553)-net in base 4, because

1 times m-reduction [i] would yield (121, 259, 1553)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 880963 569807 174383 941184 394107 111175 358404 338151 244231 591330 065981 029051 748705 198760 458230 630171 571296 141362 419091 308838 721206 359167 562571 993436 436101 992192 > 4²⁵⁹ [i]