MinT - Best Known (230−153, 230, s)-Nets in Base 4

Best Known (230−153, 230, s)-Nets in Base 4

(230−153, 230, 104)-Net over F₄ — Constructive and digital

Digital (77, 230, 104)-net over F₄, using

t-expansion [i] based on digital (73, 230, 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]

(230−153, 230, 112)-Net over F₄ — Digital

Digital (77, 230, 112)-net over F₄, using

t-expansion [i] based on digital (73, 230, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(230−153, 230, 572)-Net in Base 4 — Upper bound on s

There is no (77, 230, 573)-net in base 4, because

1 times m-reduction [i] would yield (77, 229, 573)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 836230 108610 126068 148351 444347 594054 552553 975463 966374 462726 780833 770513 775553 943859 920517 388198 659399 752332 467251 774907 703838 114308 001400 > 4²²⁹ [i]