MinT - Best Known (120, 120+134, s)-Nets in Base 4

Best Known (120, 120+134, s)-Nets in Base 4

(120, 120+134, 130)-Net over F₄ — Constructive and digital

Digital (120, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(120, 120+134, 168)-Net over F₄ — Digital

Digital (120, 254, 168)-net over F₄, using

t-expansion [i] based on digital (115, 254, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(120, 120+134, 1592)-Net in Base 4 — Upper bound on s

There is no (120, 254, 1593)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 860 759652 549268 408287 055708 878077 544068 130689 663570 371728 803368 860909 218607 580076 761455 632486 908692 861279 452833 267941 848291 395093 366819 300117 474048 941760 > 4²⁵⁴ [i]