MinT - Best Known (240−169, 240, s)-Nets in Base 4

Best Known (240−169, 240, s)-Nets in Base 4

(240−169, 240, 66)-Net over F₄ — Constructive and digital

Digital (71, 240, 66)-net over F₄, using

t-expansion [i] based on digital (49, 240, 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]

(240−169, 240, 105)-Net over F₄ — Digital

Digital (71, 240, 105)-net over F₄, using

t-expansion [i] based on digital (70, 240, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(240−169, 240, 485)-Net in Base 4 — Upper bound on s

There is no (71, 240, 486)-net in base 4, because

1 times m-reduction [i] would yield (71, 239, 486)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 803702 466672 219961 075548 017791 681592 109475 884433 349266 046107 967733 147713 395662 567480 119082 865259 573741 114206 002405 901653 029986 706402 553190 092430 > 4²³⁹ [i]