MinT - Best Known (233−116, 233, s)-Nets in Base 4

Best Known (233−116, 233, s)-Nets in Base 4

(233−116, 233, 130)-Net over F₄ — Constructive and digital

Digital (117, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(233−116, 233, 168)-Net over F₄ — Digital

Digital (117, 233, 168)-net over F₄, using

t-expansion [i] based on digital (115, 233, 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]

(233−116, 233, 1914)-Net in Base 4 — Upper bound on s

There is no (117, 233, 1915)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 192 067077 454501 267519 295080 504391 190535 071659 487685 275386 244809 207438 374235 768082 420390 853124 149019 110029 808359 938643 299591 667104 164092 138595 > 4²³³ [i]