MinT - Best Known (260−146, 260, s)-Nets in Base 4

Best Known (260−146, 260, s)-Nets in Base 4

(260−146, 260, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(260−146, 260, 165)-Net over F₄ — Digital

Digital (114, 260, 165)-net over F₄, using

t-expansion [i] based on digital (109, 260, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(260−146, 260, 1242)-Net in Base 4 — Upper bound on s

There is no (114, 260, 1243)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 574734 410856 203724 154477 239946 872609 610608 975603 515704 863010 310677 044857 238013 601537 181715 648600 094228 377941 677987 977134 949511 805564 319408 812643 802221 615450 > 4²⁶⁰ [i]