MinT - Best Known (180, 180+52, s)-Nets in Base 4

Best Known (180, 180+52, s)-Nets in Base 4

(180, 180+52, 1052)-Net over F₄ — Constructive and digital

Digital (180, 232, 1052)-net over F₄, using

trace code for nets [i] based on digital (6, 58, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(180, 180+52, 3652)-Net over F₄ — Digital

Digital (180, 232, 3652)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+52, 828682)-Net in Base 4 — Upper bound on s

There is no (180, 232, 828683)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 634452 380545 202403 253590 624004 406090 787535 982561 155999 427949 879079 141603 056386 290732 710773 824708 936825 488335 171339 881330 970526 481432 811600 > 4²³² [i]