MinT - Best Known (217−95, 217, s)-Nets in Base 4

Best Known (217−95, 217, s)-Nets in Base 4

(217−95, 217, 130)-Net over F₄ — Constructive and digital

Digital (122, 217, 130)-net over F₄, using

t-expansion [i] based on digital (105, 217, 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]

(217−95, 217, 235)-Net over F₄ — Digital

Digital (122, 217, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−95, 217, 3541)-Net in Base 4 — Upper bound on s

There is no (122, 217, 3542)-net in base 4, because

1 times m-reduction [i] would yield (122, 216, 3542)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11153 939318 219984 372331 390705 154494 667652 186146 727910 990667 995649 233813 761041 246356 288147 238101 490135 500580 018349 310648 866028 203920 > 4²¹⁶ [i]