MinT - Best Known (260−59, 260, s)-Nets in Base 4

Best Known (260−59, 260, s)-Nets in Base 4

(260−59, 260, 1052)-Net over F₄ — Constructive and digital

Digital (201, 260, 1052)-net over F₄, using

trace code for nets [i] based on digital (6, 65, 263)-net over F₂₅₆, using
- net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(260−59, 260, 3770)-Net over F₄ — Digital

Digital (201, 260, 3770)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−59, 260, 926847)-Net in Base 4 — Upper bound on s

There is no (201, 260, 926848)-net in base 4, because

1 times m-reduction [i] would yield (201, 259, 926848)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 858116 301567 292776 753013 606056 795699 844904 482545 559601 977274 241958 019227 367701 583162 378164 386296 886788 164153 997749 218953 580161 730052 544919 290208 057477 826873 > 4²⁵⁹ [i]