MinT - Best Known (105, 105+65, s)-Nets in Base 4

Best Known (105, 105+65, s)-Nets in Base 4

(105, 105+65, 130)-Net over F₄ — Constructive and digital

Digital (105, 170, 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+65, 296)-Net over F₄ — Digital

Digital (105, 170, 296)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+65, 6421)-Net in Base 4 — Upper bound on s

There is no (105, 170, 6422)-net in base 4, because

1 times m-reduction [i] would yield (105, 169, 6422)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 561798 788889 186270 294397 375482 577041 431726 796205 495940 183218 622550 494490 786147 591804 373694 739508 202920 > 4¹⁶⁹ [i]