MinT - Best Known (116, 116+144, s)-Nets in Base 4

Best Known (116, 116+144, s)-Nets in Base 4

(116, 116+144, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(116, 116+144, 168)-Net over F₄ — Digital

Digital (116, 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]

(116, 116+144, 1316)-Net in Base 4 — Upper bound on s

There is no (116, 260, 1317)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 433970 161542 581566 839170 224879 900135 610003 057370 407438 905368 144701 041307 991154 475148 518003 470467 110035 781538 783263 956042 390258 700879 422260 497655 522333 375280 > 4²⁶⁰ [i]