MinT - Best Known (105, 105+85, s)-Nets in Base 4

Best Known (105, 105+85, s)-Nets in Base 4

(105, 105+85, 130)-Net over F₄ — Constructive and digital

Digital (105, 190, 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]

(105, 105+85, 195)-Net over F₄ — Digital

Digital (105, 190, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+85, 2783)-Net in Base 4 — Upper bound on s

There is no (105, 190, 2784)-net in base 4, because

1 times m-reduction [i] would yield (105, 189, 2784)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 618203 645574 141465 819114 265399 804523 925567 789606 402101 271446 627911 212762 622678 290314 156267 986702 711550 493085 567750 > 4¹⁸⁹ [i]