MinT - Best Known (207−143, 207, s)-Nets in Base 4

Best Known (207−143, 207, s)-Nets in Base 4

(207−143, 207, 66)-Net over F₄ — Constructive and digital

Digital (64, 207, 66)-net over F₄, using

t-expansion [i] based on digital (49, 207, 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]

(207−143, 207, 99)-Net over F₄ — Digital

Digital (64, 207, 99)-net over F₄, using

t-expansion [i] based on digital (61, 207, 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]

(207−143, 207, 451)-Net in Base 4 — Upper bound on s

There is no (64, 207, 452)-net in base 4, because

1 times m-reduction [i] would yield (64, 206, 452)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11915 362977 449536 710577 257269 392172 601746 829239 617015 598886 980523 409579 409365 089078 550699 416413 667308 051097 357433 601819 820640 > 4²⁰⁶ [i]