MinT - Best Known (260−119, 260, s)-Nets in Base 4

Best Known (260−119, 260, s)-Nets in Base 4

(260−119, 260, 130)-Net over F₄ — Constructive and digital

Digital (141, 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]

(260−119, 260, 240)-Net over F₄ — Digital

Digital (141, 260, 240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−119, 260, 3294)-Net in Base 4 — Upper bound on s

There is no (141, 260, 3295)-net in base 4, because

1 times m-reduction [i] would yield (141, 259, 3295)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 861443 627915 015977 781838 129056 493173 930362 402868 580383 723349 066065 179278 566778 627927 653227 957541 194908 722063 080525 708083 055694 495623 560518 543782 987522 198240 > 4²⁵⁹ [i]