MinT - Best Known (214−91, 214, s)-Nets in Base 4

Best Known (214−91, 214, s)-Nets in Base 4

(214−91, 214, 130)-Net over F₄ — Constructive and digital

Digital (123, 214, 130)-net over F₄, using

t-expansion [i] based on digital (105, 214, 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]

(214−91, 214, 255)-Net over F₄ — Digital

Digital (123, 214, 255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−91, 214, 4120)-Net in Base 4 — Upper bound on s

There is no (123, 214, 4121)-net in base 4, because

1 times m-reduction [i] would yield (123, 213, 4121)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 174 524552 185191 702696 887238 608370 652996 936275 400151 692373 955559 804720 938554 941712 347216 359403 311220 910930 387416 954802 464462 114816 > 4²¹³ [i]