MinT - Best Known (73, 73+166, s)-Nets in Base 4

Best Known (73, 73+166, s)-Nets in Base 4

(73, 73+166, 104)-Net over F₄ — Constructive and digital

Digital (73, 239, 104)-net over F₄, using

net from sequence [i] based on digital (73, 103)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(73, 73+166, 112)-Net over F₄ — Digital

Digital (73, 239, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(73, 73+166, 506)-Net in Base 4 — Upper bound on s

There is no (73, 239, 507)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 819599 553244 307849 317338 892758 055192 453410 987415 269047 815939 165889 671027 174317 839048 326080 218142 226848 162793 837952 041587 660024 431033 621532 212884 > 4²³⁹ [i]