MinT - Best Known (232−56, 232, s)-Nets in Base 4

Best Known (232−56, 232, s)-Nets in Base 4

(232−56, 232, 1036)-Net over F₄ — Constructive and digital

Digital (176, 232, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 58, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(232−56, 232, 2491)-Net over F₄ — Digital

Digital (176, 232, 2491)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−56, 232, 366736)-Net in Base 4 — Upper bound on s

There is no (176, 232, 366737)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 636929 350826 317308 683771 201160 552079 049691 667380 095655 326193 932394 939242 052943 464717 579811 654686 048374 069498 339680 298045 070145 858374 012128 > 4²³² [i]