MinT - Best Known (229−108, 229, s)-Nets in Base 4

Best Known (229−108, 229, s)-Nets in Base 4

(229−108, 229, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(229−108, 229, 195)-Net over F₄ — Digital

Digital (121, 229, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−108, 229, 2453)-Net in Base 4 — Upper bound on s

There is no (121, 229, 2454)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 746613 547395 273196 726199 780688 014652 840196 116963 403947 242662 434786 553646 920806 416825 963380 620643 158992 011177 630390 750615 816726 635139 715680 > 4²²⁹ [i]