MinT - Best Known (229−114, 229, s)-Nets in Base 4

Best Known (229−114, 229, s)-Nets in Base 4

(229−114, 229, 130)-Net over F₄ — Constructive and digital

Digital (115, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 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]

(229−114, 229, 168)-Net over F₄ — Digital

Digital (115, 229, 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]

(229−114, 229, 1883)-Net in Base 4 — Upper bound on s

There is no (115, 229, 1884)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 745110 809340 897438 864234 788246 587047 452934 855497 216774 674293 676993 035731 466851 688636 795339 075001 890481 531243 221420 889479 853206 014164 242610 > 4²²⁹ [i]