MinT - Best Known (106, 106+111, s)-Nets in Base 4

Best Known (106, 106+111, s)-Nets in Base 4

(106, 106+111, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(106, 106+111, 144)-Net over F₄ — Digital

Digital (106, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(106, 106+111, 1601)-Net in Base 4 — Upper bound on s

There is no (106, 217, 1602)-net in base 4, because

1 times m-reduction [i] would yield (106, 216, 1602)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11327 913000 251695 207748 105624 294009 099856 942239 546910 028011 635039 327533 091577 728861 162106 568929 004706 260632 258494 333523 310528 154464 > 4²¹⁶ [i]