MinT - Best Known (131, 232, s)-Nets in Base 4

Best Known (131, 232, s)-Nets in Base 4

(131, 232, 130)-Net over F₄ — Constructive and digital

Digital (131, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(131, 232, 254)-Net over F₄ — Digital

Digital (131, 232, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 232, 3885)-Net in Base 4 — Upper bound on s

There is no (131, 232, 3886)-net in base 4, because

1 times m-reduction [i] would yield (131, 231, 3886)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 913693 759041 277212 204479 495092 362000 302775 254748 904489 429905 569748 325562 735964 441005 972890 970607 372107 935177 154329 352372 040143 622128 898656 > 4²³¹ [i]