MinT - Best Known (245−120, 245, s)-Nets in Base 4

Best Known (245−120, 245, s)-Nets in Base 4

(245−120, 245, 130)-Net over F₄ — Constructive and digital

Digital (125, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−120, 245, 184)-Net over F₄ — Digital

Digital (125, 245, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−120, 245, 2172)-Net in Base 4 — Upper bound on s

There is no (125, 245, 2173)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3256 290335 114731 030330 142380 644183 214490 032951 494160 114086 454022 260541 272925 744396 607999 413716 106504 240467 059982 544080 972119 944687 179409 371891 509715 > 4²⁴⁵ [i]