MinT - Best Known (99, 243, s)-Nets in Base 4

Best Known (99, 243, s)-Nets in Base 4

(99, 243, 104)-Net over F₄ — Constructive and digital

Digital (99, 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]

(99, 243, 144)-Net over F₄ — Digital

Digital (99, 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]

(99, 243, 933)-Net in Base 4 — Upper bound on s

There is no (99, 243, 934)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 046277 635595 783783 854449 295055 750406 945772 471010 686911 588562 113062 836486 742858 382097 184438 230304 010434 689942 069543 432454 491364 775035 532573 872840 > 4²⁴³ [i]