MinT - Best Known (243−143, 243, s)-Nets in Base 4

Best Known (243−143, 243, s)-Nets in Base 4

(243−143, 243, 104)-Net over F₄ — Constructive and digital

Digital (100, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(243−143, 243, 144)-Net over F₄ — Digital

Digital (100, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(243−143, 243, 967)-Net in Base 4 — Upper bound on s

There is no (100, 243, 968)-net in base 4, because

1 times m-reduction [i] would yield (100, 242, 968)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 488219 200758 266180 123638 230030 258785 451255 787198 864477 383305 460746 765067 513211 083124 583208 584565 763083 014363 654674 322930 574545 884515 520835 772525 > 4²⁴² [i]