MinT - Best Known (245−147, 245, s)-Nets in Base 4

Best Known (245−147, 245, s)-Nets in Base 4

(245−147, 245, 104)-Net over F₄ — Constructive and digital

Digital (98, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(245−147, 245, 144)-Net over F₄ — Digital

Digital (98, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 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]

(245−147, 245, 901)-Net in Base 4 — Upper bound on s

There is no (98, 245, 902)-net in base 4, because

1 times m-reduction [i] would yield (98, 244, 902)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 824 439387 972813 284374 333114 172260 908969 286048 171990 412874 452551 242213 085642 218607 848164 068647 450785 719496 572648 549715 096499 266595 632830 452379 677040 > 4²⁴⁴ [i]