MinT - Best Known (107, 107+146, s)-Nets in Base 4

Best Known (107, 107+146, s)-Nets in Base 4

(107, 107+146, 130)-Net over F₄ — Constructive and digital

Digital (107, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(107, 107+146, 144)-Net over F₄ — Digital

Digital (107, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(107, 107+146, 1080)-Net in Base 4 — Upper bound on s

There is no (107, 253, 1081)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 217 620754 283995 041808 918669 846367 591256 039701 455685 784023 610276 591925 548334 397235 736982 783555 164210 614416 550250 093342 657732 097085 467968 057655 216511 217600 > 4²⁵³ [i]