MinT - Best Known (244−59, 244, s)-Nets in Base 4

Best Known (244−59, 244, s)-Nets in Base 4

(244−59, 244, 1036)-Net over F₄ — Constructive and digital

Digital (185, 244, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 61, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(244−59, 244, 2581)-Net over F₄ — Digital

Digital (185, 244, 2581)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−59, 244, 431344)-Net in Base 4 — Upper bound on s

There is no (185, 244, 431345)-net in base 4, because

1 times m-reduction [i] would yield (185, 243, 431345)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 796022 311249 154745 499217 712620 808613 904639 332636 040531 808732 114474 629741 824361 019336 735403 602002 049749 586828 547855 555639 929404 654652 255305 534208 > 4²⁴³ [i]