MinT - Best Known (240−168, 240, s)-Nets in Base 4

Best Known (240−168, 240, s)-Nets in Base 4

(240−168, 240, 66)-Net over F₄ — Constructive and digital

Digital (72, 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]

(240−168, 240, 105)-Net over F₄ — Digital

Digital (72, 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]

(240−168, 240, 494)-Net in Base 4 — Upper bound on s

There is no (72, 240, 495)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 146220 298216 861061 924361 091007 143350 407261 106828 857234 729653 549437 794682 674603 661096 518449 988042 763477 615383 592687 113633 829748 633516 131215 088658 > 4²⁴⁰ [i]