MinT - Best Known (206−141, 206, s)-Nets in Base 4

Best Known (206−141, 206, s)-Nets in Base 4

(206−141, 206, 66)-Net over F₄ — Constructive and digital

Digital (65, 206, 66)-net over F₄, using

t-expansion [i] based on digital (49, 206, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(206−141, 206, 99)-Net over F₄ — Digital

Digital (65, 206, 99)-net over F₄, using

t-expansion [i] based on digital (61, 206, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(206−141, 206, 464)-Net in Base 4 — Upper bound on s

There is no (65, 206, 465)-net in base 4, because

1 times m-reduction [i] would yield (65, 205, 465)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2953 783640 859689 396752 146324 598518 322345 476452 009985 364047 898311 211198 451934 517021 690502 633829 569056 928391 497967 490471 738360 > 4²⁰⁵ [i]