MinT - Best Known (106, 249, s)-Nets in Base 4

Best Known (106, 249, s)-Nets in Base 4

(106, 249, 130)-Net over F₄ — Constructive and digital

Digital (106, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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, 249, 144)-Net over F₄ — Digital

Digital (106, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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, 249, 1094)-Net in Base 4 — Upper bound on s

There is no (106, 249, 1095)-net in base 4, because

1 times m-reduction [i] would yield (106, 248, 1095)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 210846 322482 254244 784823 497305 991457 512863 595170 510659 770328 708027 948846 405501 122219 165670 215525 432267 590845 152383 197130 462096 148566 724440 438280 527580 > 4²⁴⁸ [i]